Casimir Energy of the Universe and the Dark Energy Problem

TL;DR

This paper explores the Casimir energy in 5D universe models as a potential explanation for dark energy, introducing a new regularization method and analyzing the renormalization group flow of the cosmological constant.

Contribution

It introduces sphere lattice regularization for 5D models and demonstrates the renormalization of divergences in calculating Casimir energy.

Findings

Successfully regularized divergences using sphere lattice regularization.

Explicitly obtained the renormalization-group flow of the cosmological constant.

Numerical demonstration of divergence renormalization in 5D models.

Abstract

We regard the Casimir energy of the universe as the main contribution to the cosmological constant. Using 5 dimensional models of the universe, the flat model and the warped one, we calculate Casimir energy. Introducing the new regularization, called {\it sphere lattice regularization}, we solve the divergence problem. The regularization utilizes the closed-string configuration. We consider 4 different approaches: 1) restriction of the integral region (Randall-Schwartz), 2) method of 1) using the minimal area surfaces, 3) introducing the weight function, 4) {\it generalized path-integral}. We claim the 5 dimensional field theories are quantized properly and all divergences are renormalized. At present, it is explicitly demonstrated in the numerical way, not in the analytical way. The renormalization-group function ($\be$-function) is explicitly obtained. The renormalization-group flow of the cosmological constant is concretely obtained.